The first and the last term of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
Given: An A.P. with first term a=8 and last term l=350 and the common difference d=9
To do: To find the numbers of the terms in the given A.P. and the sum of its terms also.
Solution:
As known that $l=a+( n-1) d$ in an A.P.
On substituting $l=350,\ a=8\ and\ d=9$ as given
$350=8+( n-1) 9$
$\Rightarrow n-1=\frac{350-8}{9}={342}{9}=38$
$\Rightarrow n=38+1=39$
And we know that the sum of n terms in an A.P.,
$S_{n}=\frac{n}{2} \ ( a+l)$
$=\frac{39}{2}( 8+350)$ $( on\ substituting\ the\ values\ of\ n,\ a\ and\ l)$
$=6981$
Hence, the given A.P. has 39 terms and sum of its all terms is 6981.
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